Fair Crack of the Whip? The Distribution of Augmented Wealth in Australia from 2002 to 2018

The omission of pension wealth potentially distorts the international comparison of wealth distributions. Private pension wealth is often included in households’ wealth portfolios, while public pension claims are not. Augmented wealth, the sum of net worth and pension wealth, resolves this limitation by including the present value of social security pension wealth. This paper provides a detailed analysis of augmented wealth in Australia between 2002 and 2018, capturing the establishment of the compulsory private pension scheme, Superannuation, which was introduced in 1992. Moreover, I depict the interaction of Superannuation with the public scheme Age Pension and how that affects the overall wealth distribution. Augmented wealth in Australia is found to be less equally distributed than wealth in Germany or Switzerland, but more equally than in the United States. JEL classification: D31; H55; J32


Introduction
The analysis of wealth distributions has gained more and more attention around the world throughout the last decade. A highly unequal distribution of wealth can negatively affect growth and innovation (Bagchi and Svejnar, 2015;Berg et al., 2018) and raises concerns about an unequal distribution in welfare (Stiglitz, 2012). Pension wealth challenges the comparability of wealth data across countries. (Bönke et al., 2019;Frick and Headey, 2009;Wolff, 1996;Kuhn, 2020) Private pension wealth is often included in wealth surveys and, therefore, in wealth distributions, while public pension entitlements are not. Several studies showed, however, that public pension wealth is an (imperfect) substitute for net worth (Attanasio and Brugiavini, 2003;Wolff, 2015a). 1 Hence, augmented wealth, i.e. net worth plus private and public pension wealth, contributes to a sincere comparison of international wealth distributions incorporating a more reliable measure of economic wellbeing (Wolff, 2015b;Bönke et al., 2019). Moreover, pension wealth aggregates are a helpful tool in a panel analysis to understand the distributional effects of pension policies. This paper explores the evolution of augmented wealth aggregates in Australia between 2002 and 2018. Australia is particularly interesting for an assessment, as its pension system relies on two main schemes, i.e. the means-tested social security pension system, called Age Pension, and the private pension system, called Superannuation. Like many advanced economies, Australia struggled to provide a sustainable and effective pension scheme that secures a commensurate level of income, and, hence, consumption, during retirement. In 1992, the Australian government 2 , therefore, introduced compulsory contributions by employers to the employee's Superannuation accounts as an addition to the established, taxfunded Age Pension. Superannuation is mostly a defined distribution scheme for employees and employers and it is designed to retain and guarantee the standard of living for future retirees (Superannuation (Objective) Bill, 2016).
This analysis provides a deeper understanding about the establishment of the Superannuation scheme. It comprises of two main components: first, I describe income during retirement. This includes the analysis of dissaving patterns of Superannuation accounts and how they interact with the Age Pension scheme. Second, I analyze augmented wealth in Australia over time by focusing especially on the development of the pension schemes.
I use the Household, Income and Labour Dynamics in Australia survey, which provides five wealth modules at the household level between 2002 and 2018 (Watson and Wooden, 2002). Furthermore, it includes exhaustive pension information at the individual level. I find that Australian households, especially those with a household head aged 50 and older, realized significant wealth gains between 2002 and 2018. Despite large wealth increases, inequality remains stable in Australia. The results show that Age Pension remains the most important source of income for most retried Australians, though income from Superannuation has increased its share. Social security pension wealth is the largest asset category at the lower end of the wealth distribution. Pension wealth has an equalizing effect, as the Gini index in 2018 reduces from 0.66 for net worth to 0.571 for augmented wealth. Comparing my findings to Germany, Switzerland, and the United States (US) (Bönke et al., 2019;Kuhn, 2020), Australia's Gini index of augmented wealth is the second highest after the US. Furthermore, I find evidence for behavioral responsiveness from the interaction between Superannuation and Age Pension, as individuals dissave Superannuation accounts faster when they are also eligible for Age Pension. My results also raise concerns as to whether the retiree population will diverge between those depending on Age Pension and those relying on Superannuation.
Despite the increased data availability, the role of pension wealth in wealth distributions has been marginally studied. Harding (2002) analyzes pension wealth, especially Superannuation accounts in Australia, and finds that the scheme reduces wealth inequality while overall wealth inequality remained constant between the 1980s and the 1990s. Frick and Headey (2009)  This paper contributes to the existing literature by taking a first look at augmented wealth in Australia. Furthermore, I present a primary inter-temporal analysis of social security pension wealth. To the best of my knowledge, I am also the first who empirically assesses the dissaving behavior of public pension scheme after retirement. Moreover, this paper also contributes to the understanding of the enrollment phase of a new private pension scheme, and the lessons to be learned for other economies.
The remainder of this paper is as follows: Section 2 describes the Australian pension system in detail, Section 3 provides the applied methodology, Section 4 depicts the data, Section 5 presents the empirical findings, and Section 6 provides a discussion and concludes.

Australian Pension System
This chapter provides a detailed overview of the Australian pension system. It builds on two main pillars: the social security scheme Age Pension and the private Superannuation scheme. 3 The Australian pension system contains several unique features. First, the means-tested social security pension is tax-funded, which does not rely on individuals employment history, but on an income and asset test at retirement. Second, the private occupational pension scheme Superannuation became compulsory in 1992 to provide additional incentives to built up private pension wealth (Australian Government, 1992).
Third, Age Pension and Superannuation are not independent, but interact with each other.
Wealth and returns from Superannuation alter an individual's eligibility to Age Pension.
In this section, I describe the institutional settings of the different schemes and what has changed between 2002 and 2018. 4

Age Pension
General information The Age Pension scheme is a tax-funded, means-tested social security scheme. Individuals or households, who pass the income and asset test, are eligible to Age Pension at the age of 65 to 67. Additional to the full basic rate, which was $629 5 for singles and $834.40 for couples per fortnight in 2018, the Australian government provides several further payments, i.e. Rent Assistance, Energy Supplement, and Pension Supplement. 6 Moreover, individuals are entitled to the Pensioner Concession Health Card, providing higher refunds for health care costs. Depending on the state, local councils also offer additional discounts on property and water rates, public transport fares or motor vehicle registration.
Eligibility conditions The first hurdle for being eligible to Age Pension is the retirement age and the residency in Australia. In 2018, the retirement age was 65 for both genders, i.e. cohorts born in 1953 or earlier. The residency rules demand that an individual has been living in Australia for at least ten years in total, with five of these years without a break (Australian Government, 2018).
Income and asset test Singles or couples, who reached the retirement age and meet the residency rules, are eligible to Age Pension, if they pass the income and asset test. The income test includes gross labor earnings, pensions, received gifts, rental income, as well as financial gains. Retirees are allowed to work during retirement, but labor income above the work bonus, i.e. $250 per fortnight, is included in the income test. The income test does not consider realized, financial returns, but imputed, "deemed" returns on the basis of total financial assets (Australian Government, 2021b). 7 The Australian government provides low and high interest rates 8 , which are multiplied with the value of the financial assets below and above the threshold, respectively. The deeming rates are adjusted on a non-regular basis by the Australian tax authorities (Australian Government, 2021a). The asset tests inquire the level of net worth, including real estate, business assets, financial wealth, Superannuation accounts, and valuables. Real estate does not include the principle home, however different thresholds apply for homeowners and non-homeowners, providing a higher allowance for the latter. In 2018, the total wealth threshold for the full pension 4 The information presented in this section is based on several documents and websites provided by the Australian Government (2018Government ( , 2021b. 5 1 AUD = 0.7405 USD = 0.6325 EUR in 30th June 2018. 6 In 2018, Rent Assistance added up to $128.00 ($135.80) for singles (couples) per fortnight, Energy Supplement another 10.60 ($14.10) , and Pension Supplement $51.10 ($67.80) . For more information, the Table A1 in the Appendix. 7 The corresponding asset base includes the market value of savings accounts and term deposits, managed investments, loans and debentures, listed shares and securities, gifts, and Superannuation accounts.
8 Also called deeming rates: lower rate was 1,75 percent, higher rate was 3.25 percent per year in 2018.
for singles (couples), without owning their home, was at $465,500 ($594,500), whereas home-owners were allowed to own $258,500 ($387,500). 9 Full vs partial pension Individuals and couples can qualify for a full or partial pension, depending on their level of income and wealth. Once they earn more than the first threshold, i.e. $172 ($304) per fortnight in 2018, every additional dollar reduces the payment by a reduction rate, which was for singles (couples) 0.5 (0.25) in 2018. The wealth thresholds for the partial pension are considerably higher than those for the full pension, 9 This shows that the scheme considers sharing resources of couples, and therefore provides lower payment and lower threshold, compared to two single individuals. which were $771,000 ($1,055,000) for non-homeowners, and were $564,000 ($848,000) for homeowners. There are strong incentives to be at least partially eligible to Age Pension, even if the payment is low, as they are eligible to the benefits of the Pensioner Concession Health Card.
Changes between 2002 and 2018 There were several policy changes and adjustments in the Age Pension scheme. The Age Pension benefits, as well as the income and asset test thresholds, are adjusted bi-annually. 10 Table 1 depicts the changes of rates and thresholds valid in July of the years included in my analysis. The threshold for income tests increased steadily over the years, however, those for the partial pensions nearly doubled for singles, whereas those for couples increased by around two-thirds. The asset thresholds increased relatively steadily too, but were actively adjusted by the Federal Government in 2017: the full pension thresholds were increased, while the thresholds for the partial pension were reduced, explaining the difference between 2014 and 2018, provided in Table   1. Between 2006 and 2010, the reduction rate for the partial pension increased from 0.4 to 0.5 (0.2 to 0.25 for couples). The Age Pension payments were additionally increased in 2009 (Australian Government, 2009).
At the beginning of the observed period, in 2002, women could qualify earlier for Age Pension than men. The transition of the retirement age for women increased from 60 to 65 by 2014. Another transition for both women and men started in 2018, which will gradually raise the retirement age to 67 by 2024. The 2018 wave is partially affected, as the retirement age for those born after July 1952 and before 1954 can retire at the age of 65 and a half.

Superannuation
General information The Superannuation scheme represents, for most Australians, an investment in an accumulation fund. 11 The fund can be managed by financial institutions (retail funds), by the employing company (corporate funds) or industry (industry funds), by the public sector for civil servants (public sector funds) and by the individuals themselves (self-managed funds). 12 The total wealth in Superannuation accounts was $2.9 trillion in 2019 (ASFA, 2021), i.e. 1.3 times the annual Australian GDP.
The choice of the Superannuation fund is not always subject to the employee, since enterprise agreements can specify the fund type. 13 The Australian government sets standards for contributions by employees and compulsory monthly contributions for employers, i.e. the Superannuation Guarantee, which is at least 9.5 percent of the monthly wage in 10 Until 2007, this was done on the basis of the Consumer Price Index (CPI). After the introduction of the Pensioner and Beneficiary Living Cost Index (PBLCI), the rates are increased by whichever index is greater.
11 Even though Australians potentially possess several Superannuation funds, I refer to them in singular. 12 Industry and retail funds include more than 11 million members each out of a total 27.4 million accounts, and are the most dominant fund categories in 2019 (Australian Prudential Regulation Authority (APRA), 2021).
13 This affects around 30 percent of all receivers (Australian Government, 2021b). Theoretically, employees could set up their own fund and transfer the money from the default fund. However, this is costly. I gratefully thank Roger Wilkins for this remark.
2018. 14 Additionally, individuals can invest further savings from their gross or net income. The withdrawal after the preservation age, i.e. 60 in 2018, is unlimited and free from income taxes. 15 Low income earners qualify to a governmental supplement contribution match of 50 percent, capped at $500 per year.
Superannuation and taxation Superannuation savings are liable to tax (Australian Tax Office, 2021). The tax rate depends on the type of contribution. Most commonly, contributions are taxed lump-sum at 15 percent. These are "concessional" contributions including the compulsory payments by the employer 16 and additional private investments up to $25,000 per year from the gross income. The "Division 293 tax" raises the tax rate to 30 percent for individuals earning more than $250,000. Additional "Non-concessional" contributions are not taxed, as they stem from net-income. However, they are capped at $100,000 per year in 2018 and only allowed for those with less than $ 1.6 million wealth in Superannuation accounts. Any contribution above is taxed at the marginal income tax rate. 17 Except in rare circumstances, e.g. due to medical conditions, individuals cannot access their Superannuation accounts before they reach the preservation age, without paying marginal income tax rates. Self-managed funds can also borrow a loan against its Superannuation, before preservation age is reached. Generally, returns on Superannuation investments are taxed at a 15 % tax rate 18 , while returns on the first $1.6 million are not taxed if they are realized in the retirement phase. The reduced taxation rate is the main vehicle to incentivize savings throughout the accumulation period. The taxation of Superannuation investments and returns is, at 15 percent, considerably lower than the marginal income tax rates, which includes income from 14 The employer has to contribute quarterly. Delayed payments are taxed with the 10 percent Super Guarantee Charge. The term "Guarantee" can be misleading, as it may imply a defined benefit later in retirement. However, it describes the monthly contribution to the Superannuation scheme and does not represent a "guaranteed" income flow during retirement.
15 Exceptions apply for individuals holding an untaxed super fund (contributions are not taxed), which can occur in the case of a public sector fund. However, the tax rate does not depend on the withdrawal sum for retired Australians. 16 The contribution is deductible for employers at the end of financial year. 17 These tax rates are calculated at the end of the financial year. As income taxes are normally paid directly, this can delay tax payments. Therefore, the Australian government introduced the Excess concessional contribution charge rates, which adds an extra rate on the marginal income tax (4.96% in 2018). 18 Australian Tax Office applies a dividend imputation system, meaning that tax payments, e.g. by the share emitting company, can be used by the shareholder to offset their own tax liabilities. It potentially decreases the tax rate for the Superannuation owner. capital gains. In Australia, there is no separate tax rate on capital gains, as it is added to labor income and other income sources. The total sum defines the individual tax rate. Table 2 provides the tax brackets and the corresponding tax rates for the years 2002 and 2018. The brackets increased significantly in the considered period and the tax rates were raised at the lower end and decreased at the top. As the Division 293 Tax does not apply for individuals with an income below $250,000, the tax advantage from Superannuation savings is substantially higher at the upper end of the income distribution.

Changes between 2002 and 2018
In the beginning year of my analysis, the compulsory Superannuation scheme was ten years old and therefore relatively new. Several policy changes and adjustments have been made in the successive years, of which several were of a larger scale. This includes the raise of the preservation age, changes to the concessional contributions cap, the abolition of Reasonable Benefit Limits, the end of the Superannuation surcharge in 2005, and the introduction of the Division 293 tax.
In 1999, the preservation age was gradually increased from age 55 to 60. Those born before 1960 could access their Superannuation savings at 55, however the preservation age increased year by year to 60 for those who were born after June 1964. This means that from 2015 onward, individuals access their accounts a year later. An even more substantial change could be the reduction of the concessional contribution cap. As shown in Table 3, the cap was reduced from $100.000 to $25.000 in the 2010s. Moreover, the age specific caps were abolished. As a consequence, the potential tax advantages per year for Superannuation savings are significantly lower compared to end of the previous decade. On the other hand, the Reasonable Benefit Limits were abolished in 2007, which conditioned the concessional tax rate limits to wealth levels in Superannuation accounts. 19 Another considerable change was the abolition of the Superannuation Surcharge in 2005, which increased the tax rate by 12.5 percent, applied to contributions from individuals earning more than $121,075. Nonetheless, in 2012, a new type of surcharge tax was introduced, the Division 293 tax. It increases the Superannuation tax rate by 15 percent for individuals earning more than $250,000 ($300,000 until 2017). In July 2017, the Australian Tax Office introduced the $1.6 million cap to the tax-exempt status, with a 15 percent tax rate for the amount above. 20

Interactions between Superannuation and Age Pension
The Superannuation system was introduced to address the aging population in Australia, as in most advanced economies. An aging society with increasing live expectancy could bring a singular tax-based pension scheme as Age Pension to its limits. Superannuation was set as an additional pillar to support private wealth accumulation (Australian Government, 1992

Other Schemes
Besides Age Pension, the Australian government provides several other pension schemes. 22 The Disability Pension is available to compensate veterans and their partners and/or descendants for injuries or diseases caused or aggravated by war service or certain defense service. Disability Support Pension is for people aged over 16 and below retirement age with a physical, intellectual or psychiatric impairment that prevents them from working, or being re-skilled to work. Mature Age Allowance is a bridging income support payment for individuals of at least 60 years of age until they reach the retirement age. A Service Pension is paid to veterans at the same level, but five years earlier than, the Age Pension. The War Widow's/Widower's pension is paid to widowed partners and dependents of veterans. Widow Allowance is a means-tested benefit for women (born on or before 1 July 1955) widowed, divorced or separated after turning 40, working less than 20 hours per 21 Originally, the contribution per invested $ 1 was $1.5, but reduced to $0.5 in 2018. 22 Additional information on pensions are taken from Australian Government (2018). A detailed overview is provided by Harmer (2008). week. Wife pension used to apply to female partners of recipients of Age Pension where those partners were not eligible in their own right for another pension. Given a relatively high immigration rate, Australians potentially receive pensions from other governments. 23

Methodology
In this Section, I provide the definition of augmented wealth and its underlying aggregates

Wealth Aggregates
The augmented wealth definition applied here is closely related to the definition established by Bönke et al. (2019). I define the same 15 wealth aggregates as listed in Table 5.
While aggregates w1 to w10 are standard for the distributional analysis of wealth, aggregates w11 to w15 allow for a broader perspective on wealth endowments. Private pension wealth, w13, represents wealth in Superannuation funds, which potentially is included in financial assets in standard wealth analysis. The w12 aggregate represents the present value of discounted income flows from social security pensions, listed in Table 4 above. In other words, the value considered as social security wealth is the actuarially fair, discounted price to which an individual would sell their social security pension claims on complete capital market. Hence, the measure incorporates social security entitlement as the present value of pension p for individual i in year y, and is defined as where T is the "end-of-life" period, when the individual reaches the age of 100, r is a constant discount rate, i.e. 2 percent. d P t,i,y is equal to 1 if individual i is eligible for pension p in period t. pension p t,i,y represents the pension entitlement and σ t,g,c,y is the Other real estate w3 Tangible assets (collectibles) w4 Business assets w5 Financial assets w6 Total gross wealth (sum up w1 to w5) w7 Mortgage debts -owner-occupied property w8 Mortgage debts -Other real estate w9 Consumer debts w10 Net worth (w6-(w7 + w8 + w9)) w11 Statutory pension wealth without survivor benefits w11s Statutory pension wealth from survivors benefits w11d Statutory pension wealth after dissaving Superannuation accounts w12 Social security pension wealth (w11 + w11s + w11d) w13 Occupational and private pension wealth w14 Pension Wealth (w12 + w13 ) w15 Augmented wealth (w10 + w14) Notes: Description of the 15 wealth aggregates according to Bönke et al. (2019), p.12. This analysis adds w11d, which includes statutory pension wealth, which households may are eligible to after dissaving their Superannuation account.
probability of staying alive in period t depending on gender g in cohort c in year y. The Individuals receiving Age Pension could potentially lose their eligibility, from one period to the next, if they failed the income and asset test, e.g. by starting to work or having increased capital gains. This is however rare. 25 A reasonable concern could be that individuals lose their Age Pension eligibility due to policy adjustments. As the accrual method relies on the expected value of futures pension schemes, it does not include future policy changes in year y. Once these changes are introduced, they affect the present value calculation.
The statutory pension wealth from survivors pension (w11s) includes the Widow Allowance, the only scheme where the payment pension p t,i,y depends on the male partner's survival probability. Eligibility is conditioned on being female, born on or before 1 July 1955, being widowed, divorced or separated since turning 40. Women have to meet the requirements of the income and assets test and meet residence rules, i.e. living in Australia for at least 10 years. In equation 1, this means that the survival probability is, therefore, (1 − σ t,m,c,y ) × σ t,f,c,y . 26 The economic relevance remains small, as only 0.2 percent of the whole population was eligible in 2014, and the program stopped in 2018.
Including social security pension wealth and its effect on Australian wealth inequality builds the basis of the contributions of this paper. As social security pension wealth is 25 I provide more evidence for this in Section 4 and 5 26 I refrain from including divorce rates and focus on survival probabilities. financed with taxes, the contribution to the tax system is indirectly included in the classical wealth analysis. Social security pension wealth increases tax rates, which potentially reduces household net incomes and, eventually, hinders wealth accumulation compared to a situation without a tax-based pension scheme. It potentially affects the wealth aggregate directly, as it reduces net-wealth. Incorporating social security pension wealth, therefore, provides a more accurate wealth measure as it includes the benefits of the pension system.
Even though my methodology is closely related to the ones by (Bönke et al., 2019;Kuhn, 2020), the peculiarities of the Australian pension system compared to Germany, Switzerland, and US cause some deviation. The social security schemes in these three countries are pay-as-you-go schemes relying on individual labor income histories and associated pension contributions. Hence, they can calculate the present value of their pension contributions at any point in their life cycle. In these countries, tax-funded social security pensions exist as a basic income support for those who received a lower lifetime income.
As these payments are not per se a pension scheme, they are not included in the present value calculation by (Bönke et al., 2019;Kuhn, 2020). However, in my analysis, I include them in the present value calculation, because Age Pension is the major social security scheme in Australia. As I cannot observe whether cohorts below the retirement age will qualify for Age Pension, I only include their savings in Superannuation accounts.
Calculating dissaving rates and aggregate w11d Another central aspect is the interaction between Age Pension eligibility and Superannuation wealth. Once individuals reach the preservation age, the government lets individuals choose how much they retrieve per year. As Superannuation is included in the Age Pension income and asset test, there can be an incentive for those who are slightly above the income and wealth thresholds, to dissave Superannuation wealth at a higher rate. Contrary to other financial assets, this would not affect the individual tax rate 27 and one could potentially fulfill the income and asset test requirements. For this reason, I run an artificial income and asset test for those who reached the retirement age and meet the residency rules. I calculate the average Superannuation dissaving rate ν c,y for each cohort c in year y: with y s i,c,y describing the annual annuity retrieved from Superannuation wealth by individual i, and w s i,c,y representing the individuals total Superannuation wealth. N c,y is the total size of cohort c in year y. I assign the average dissaving rate to those individuals who would pass the artificial income and asset test by reducing their Superannuation in each period of the present value calculation in Equation 1. Aggregate w11d is then calculated as the present value similar to the other pensions in Equation 1. As soon as individuals are eligible, the dummy variable d P t,i,y switches from 0 to 1 and the individuals receive pension p,imputed t,i,y from this period onward. 28 27 E.g. returns from selling shares falls under the capital gain tax. 28 This affects 7.91 percent of households with a retired household head in my working sample.

Analysis of Dissaving Rates
I shed more light on the interaction between the two main pension schemes by scrutinizing dissaving rates. While saving for retirement has been addressed exhaustively in empirical analysis, dissaving dynamics during retirement has been covered far less. Dissaving decisions play a vital role for consumption smoothing. Retired households have to take the probability of their own life expectancy into account. Moreover, they potentially face new risk types, e.g. health risk, which could affect their income and, consequently, consumption.
An interesting feature of the Superannuation scheme is the flexibility once an individual reaches the preservation age. While many rules apply during the accumulation phase, individuals are free to choose their income stream in retirement. Moreover, Australians can retrieve the full amount at once without any financial losses. Furthermore, the tax advantages from the Superannuation scheme leave little incentives to transfer wealth away to other financial investments. Analyzing these private dissaving rates helps to understand how they vary across several socio-economic characteristics, e.g. age, household types, education, and wealth endowments. Moreover, I show that households, who become eligible for Age Pension at one point in retirement, follow the incentive to dissave more.
I estimate a pooled fractional probit model. The advantage of this, is that compared to a binary probit model, I can take the intensive margin of the continuous dissaving rate into account. The fractional probit model was introduced by Papke and Wooldridge (1996), who analyze aggregated employee participation rates in 401(k) pension plans in the US.
The model has the following form: where ν i represents the dissaving rate, and X h represents a set of the covariates of individual i and the intercept. Φ() represents the standard normal cumulative distribution function.

Data
The main source of my analysis is the Household and Income Dynamics in Australia (HILDA) Survey (Watson and Wooden, 2002). Additional data on the income and asset testing, as well as payments of the Age Pension scheme is taken from the Australian Government (2018). This section describes the HILDA dataset, especially in regards to the wealth modules. Furthermore, I define the working sample for the analysis of Superannuation dissaving rates.   (Hagenaars et al., 1994). Net worth provided here follows the definition of the HILDA Survey which includes Superannuation wealth (Wilkins et al., 2020). All statistics are based on imputed values. Bootstrapped standard errors in brackets using 1000 replica weights (Efron, 1979). Source: HILDA Survey wave 18. Wealth data based on survey information comes with the caveat, that the top one percent are difficult to capture adequately (Eckerstorfer et al., 2016;Kennickell and McManus, 1993). Oversampling of the rich potentially addresses this problem (Kennickell, 2008)  The mean annual dissaving rate in the working sample is slightly higher than the one in the full sample. This is due to the fact that the observations outside of the working sample have primarily missing values, and some zeros. The latter is the case, if individuals claim zero values for both income from Superannuation and wealth in Superannuation accounts.
More than thirty percent of the full retired population receive income from Superannuation

Empirical Findings
This section provides the results of my analysis and it is divided into two major subsections scrutinizing income during retirement and augmented wealth inequality. The first subsection provides an overview of the main income sources during retirement over time.
I also provide the results of my inquiry on Superannuation dissaving rates. Hence, the first subsection focuses on the retired population only. The second subsection analyzes augmented wealth inequality, focusing on the contribution of the pension schemes and describing differences across age cohorts, and sets the results within the context of augmented wealth in Germany, the US (Bönke et al., 2019), and Switzerland (Kuhn, 2020).

Income during Retirement
This subsection sheds light on the general ramifications of the main pension schemes' relevance for the retired population. The relative importance of the Superannuation scheme rises significantly during the 2002 to 2018 time span. Figure 1 provides the proportion of retired households with a household head at 55 years of age or higher, who receive at least some Age Pension or withdraw some positive annuity from their Superannuation account.
The proportion of recipients of Age Pension is relatively constant at around 50 percent throughout the considered years. The proportion of those withdrawing Superannuation annuities, however, increases from around 26 percent to 40 percent. The dominant factor for the increase is the establishment of the scheme: retired individuals in 2018 were enrolled for a longer time span throughout their life-cycle in comparison to those in earlier years.
Although the establishment of the scheme was affected by the general financial crisis (GFC) at the end of the 2000s, it did not stop its growing relevance.

Income and Gross Wealth
Even though the Age Pension and Superannuation are the main source of income in retirement, income from private investments, rent and, to some extent employment, are further sources of income. Nonetheless, they contribute differently for households along the wealth distribution. I present the income means and ratios to overall income along the gross wealth distribution in Figure  Moreover, Superannuation annuities are used to calculate the dissaving rates, which are analyzed later in this subsection.
The upper two panels describe the absolute mean values for income from public transfers, private investments, rental income, and employment. Age Pension payments remained relatively stable while Superannuation annuities increased considerably over the 16 years.
The mean income from private investments increased only for the upper 30 percent of the wealth distribution. Rental income stayed relatively constant and is equal to 0 for most households and, again, is more important for the upper 30 percent. This is not surprising, as additional housing wealth investments for rental purpose mainly appear at the top of the wealth distribution. Income from employment, which is earned by non-retired partners or children in the household, slightly decreased over time. 30 The lower two panels of Figure  Net worth and Superannuation wealth are divided by $100,000. The MEM of net worth is statistically and economically zero. Wealth levels of financial assets and housing investments are included in net worth and they do not seem to drive the individual dissaving rate decision in this specification. 32 Superannuation wealth, however, is negatively associated with the saving rate. An increase of $100,000 decreases the dissaving rate at the means by 4.51 percentage points. One reason for this is potentially the rising importance of other income sources at the higher end of the wealth distribution, as shown above. Moreover, 31 The OLS regression provides a similar effect size, which is provided in Appendix B 32 This result comes with the caveat, that net worth is measured on the household level. By sharing resources, many components could affect the individuals dissaving decission, e.g. joint consumption decisions or tax-considerations. Therefore, the true net worth effect is difficult to classify from this model specification. If only financial wealth or additional housing wealth is included, instead of net wealth as a covariate, the coefficient remains around zero. Regression result are available upon request.   The socio-economic characteristics show that women do not dissave significantly differently from men. Single households extract slightly less then those living in coupled households, but the estimate is only significant at the five percent level. A negative coefficient could indicate higher exposure to income risk, as household pooling is not possible, therefore choosing more prudent rates. The age dummies reveal a clear increase in age, significant from the 75-79 bracket. A credible factor would be the decreasing insecurity over an individual's life expectancy. A bequest motive could limit, however, the excess of the dissaving rate, as Superannuation wealth is not subject to inheritance or other additional tax that affects the transition to the closer kin. Individuals with a medium level of education, here classified as at least 12 years of schooling and less than a bachelor degree, as well as those with a high level of education, i.e. bachelor degree and above, dissave relatively more. It is not straightforward to qualify the result, as a higher dissaving rate is per se not more or less efficient.

Receive Age Pension
I also include year dummies in the regression, showing that the year-specific conditional mean of the dissaving rate reduces over time. This is may be explained, again, by the growing maturity of the Superannuation scheme associated with increasing life expectancy.
Naturally these are long-term trends and, therefore, probably do not dominate the choice of the decision rate.
From this subsection, I conclude that Age Pension remains by far the most important payment for individuals and households, with income from Superannuation accounts following second. Further, I focus on the dissaving rate of Superannuation wealth and find evidence for individuals reactions due to the provision of Superannuation wealth and income in the Age Pension eligibility test. The income and asset tests can be considered as an indirect tax on Superannuation wealth, as it reduces or hinders social security payments, but only for some, i.e. for those who would receive the full or partial pension without Superannuation wealth in the picture. This bears three major concerns: first, minimizing the tax burden, the policy may force individuals to choose inefficient dissaving rates, in regards to consumption smoothing or insurance decisions, especially at the wake of increasing health risks with age. This could induce welfare losses. Second, the policy may encourage individuals who are potentially eligible for Age Pension to reduce contribution to their Superannuation scheme before they reach the retirement age. As the contribution is linked to the employment status, this could lead to distortions, i.e. lower supply at the labor market. Third, in combination with the nearly unlimited access after the preservation age, this could contribute to tax evasion strategies, transferring wealth into less traceable means, i.e. cash or wealth in accounts overseas.

Augmented Wealth Inequality
This subsection describes augmented wealth inequality from several angles. Aside from basic statistics of the wealth aggregates, I show portfolio shares along the wealth distribu-tion over time, a Gini decomposition, and illustrate wealth levels along several household characteristics, e.g. age and household types.   Table 8 also shows the relevance of pension wealth, as the mean of augmented wealth is 45 percent higher than net wealth in 2018.

Descriptive Statistics
The pension schemes were affected by several policy adjustments and they may help to explain the changes over time. The rise of the retirement age for women and the biannual adjustments of the thresholds and pension payments contribute in keeping the social security pension wealth values stable, even though the numbers of retirees has increased.
The relatively steep upturn between 2010 and 2014 is likely due to a composition effect. The retirement age for women was successively increased from 60 to 65 until 2014. Therefore, several women had to postpone their retirement and become eligible in that year. The decrease of the mean from 2014 to 2018 might be a consequence of the rather large threshold adjustment by the government and the first step of increasing the retirement age to 67 for 33 Henceforth, w11s and w11d are not presented separately. 34 This is also shown by Wilkins et al. (2020). men and women. Major changes of the Superannuation scheme, like the reduction of the concession cap in the early 2010s, almost certainly reduced the Superannuation wealth growth. However, the results do not provide a counterfactual scenario, which would also be difficult to disentangle from the aftermath of the GFC at that time. The increase of the preservation age between 2014 and 2018 possibly increases wealth in Superannuation accounts, as the accumulation phase is prolonged. Again, which is difficult to disconnect from the developments of international stock markets, that significantly rose in that period.
Looking beyond the mean, Table 9 provides the mean, median, 25th-, 75th-, and 90th percentiles of selected wealth aggregates in 2018. Typical for net worth is having a much lower median than the mean, indicating a highly rightly-skewed distribution, with $35,000 at the 25th -, $858,900 at the 75th -, and $1,718,000 at the 90th percentile, respectively.
It also provides the ratio of households which hold a positive amount in the wealth aggregate. For net worth in 2018, these were 90.51 percent of all households. Social security pension wealth applies for 21.14 percent of Australian households. Superannuation is much more dominant in comparison to the social security pensions, but it's distribution is rightly-skewed as well. 84.88 percent of Australian households hold at least some wealth in Superannuation accounts. Augmented wealth is considerably higher than net worth for all statistics shown in Table 9 , and only 3.8 percent of all households do not possess positive augmented wealth.

Wealth Portfolios
The analysis of wealth portfolios shows the relative importance of different wealth components along the gross wealth distribution over time. Figure 4 depicts four graphs plotting the mean wealth portfolio shares for households below the 25th percentile of the gross wealth distribution ("the poor"), for those between the 25th and the 75th percentiles ("the middle"), for those between the 75th and the 90th percentile ("the upper middle") and those above the 90th percentile ("the rich"), respectively. For the sake of clarity, all components are divided by the year and group mean of augmented wealth. 35 As debts are included, the shares can be larger than 1. Moreover, the mean age of the household head for each group at each wave is provided at the right y-scale.
The figure reveals that the portfolio composition and the relative importance of pension wealth vary along the distribution. The first panel shows that pension wealth is the most important wealth component for "the poor" and this finding is consistent over time. The Superannuation wealth share increases from 35 percent to 46 percent for "the poor". Social security is the most important asset at the lower end of the wealth distribution share, i.e. 56 percent of augmented wealth in 2002, decreasing slightly to 53 percent in 2018.
This changes for "the middle class" group in the second panel, where housing becomes the most important wealth component and the relative importance of pension wealth decreases relatively to "the poor". Financial assets play a bigger role from here, but are still less important than pension wealth for "the middle class". Housing wealth remains by far the most significant wealth aggregate for "the upper middle" and "the rich", the relevance of social security pension diminishes. Furthermore, the proportion of financial assets increase in the portfolio. The relative importance of Superannuation reduces for "the rich" category, 35 Tables and graphs with monetary values are provided in Appendix C.  where its share decreases while business investments and financial assets increase their share, respectively. 36 The portfolios provide consumption -, business/HECS 37 -, and housing debts. Consumption debts are the main source of debts for the lower end of the wealth distribution, which is replaced by housing debts for the wealthier groups. Business/HECS debts are of minor relevance for all groups, compared to the other debts and wealth sources.
The four panels also show the age gradient for each group in each wave. "The poor" household heads are on average around 40 years, hence, considerably younger than those in the upper parts of the gross-wealth distribution. As wealth accumulation continues throughout the working life, some households in "the poor" group potentially end up in one of the groups above in the following years. However, as social security pension wealth is only provided for retirees, there is also a considerable fraction of older household heads in "the poor" group. Furthermore, the age difference is relatively small between "the middle", 36 Similar patterns were found in the US by Kuhn et al. (2017). 37 Stands for "Higher Education Contribution Scheme" and includes tertiary education fees "the upper middle", and "the rich". Life cycle accumulation patterns do not seem to be a main determinant as to whether a household belongs in one of these three groups.
These portfolio patterns contribute to the understanding how relevant social security pension wealth is for the lower end of the distribution, especially compared to Superannuation wealth for "the poor". Nonetheless, this could change in the years to come, as Superannuation wealth is constantly increasing its share. This offsets some of the distributional consequences of the housing boom, as they are not captured by this group. Even in "the middle", social security pension wealth plays a vital role. Financial assets and business investments seem to be an aggregate rather for "the upper middle" and "the rich".
The Superannuation scheme has increased wealth for all four groups, which points to the success of the scheme during the considered periods. However, it is still open to debate whether these gains would have occurred in other financial assets, if the scheme had not been introduced.

Wealth Modules and Inequality
I continue with the description of the wealth aggregate distributions over time. The distribution of wealth in Australia has been studied before. Using data of the Australian Bureau of Statistics (ABS), Harding (2002) finds a net wealth Gini coefficient at 0.64 in 1986 and in 1998, which remained constant due to the equalizing effect of the Superannuation accounts. Later studies reveal estimates between 0.6 and 0.65 using ABS data (Kaplan et al., 2018) or HILDA data (Headey et al., 2005;Frick and Headey, 2009;Sila and Dugain, 2019;Wilkins, 2016). The trends over time are, however, controversial as Kaplan et al. (2018) describe increasing inequality, while Sila and Dugain (2019)    and it is, in advanced economies, associated with growing wealth inequality during the last decades (Islam and McGillivray, 2019;Stiglitz, 2012), as economic growth is more beneficial to high-income-earners, and they choose higher saving rates (Saez and Zucman, 2016). This does not seem to hold for Australian households. The share of households in the sample which possess zero net worth or less has, however, increased from 7.66 to 11.10 percent. Hence, the economic growth does not seem to coincide with a broader accumulation of wealth. 39 Going beyond the Gini coefficient, I provide percentile ratios to investigate the tails of the net worth and augmented wealth distribution. Figure   38 Corresponding estimates are provided in Appendix D 39 To further investigate the contribution of net worth and pension wealth to the overall augmented wealth inequality, I apply a factor decomposition of the wealth aggregates in Appendix E. The decomposition originates from Lerman and Yitzhaki (1985) and is applied in the same context by Bönke et al. (2019).
40 I choose those percentiles as they guarantee that individuals hold some positive wealth at the lower end. Table A5 in Appendix F shows the corresponding numbers for all pension wealth aggregates. Effective distributional consequences from policy changes of the Age Pension or Superannuation scheme cannot be clearly identified in this section. This, however, does not mean that they do not occur, as the estimates presented here assess overall wealth inequality. Adjustments of the pension scheme may take more than the observed years to reveal long-term consequences.
It is important to keep in mind that the applied wealth data is top coded and survey data potentially does not capture the top adequately. This may explain why other datasets show a more significant increase of inequality in the same period (Australian Bureau of Statistics, 2021a). The 90/50 percentile ratio also hints towards a larger variation at the top. It also shows that including social security pension wealth affects the level, but not trend of inequality, as its contribution is relatively constant over time and plays no role at the top of the wealth distribution.
The assessment in this subsection shows, that Superannuation has not hitherto increased overall wealth inequality in the considered periods and its compulsory component supported a broad range of households to accumulate wealth for retirement. There is some indication that this could change in the future. Figure 6 provides generalized concentration curves of Superannuation wealth along the population ordered by augmented wealth.
The cumulative mean of Superannuation increased more at the upper end of the augmented wealth distribution, while over 15 percent did not accumulate any Superannuation wealth at all. This pattern is not surprising, as the Superannuation Guarantee depends on monthly labor income, which is highly correlated with wealth. Moreover, the tax incentives are higher for those at the upper end. Even though the maximum contribution cap was reduced in the 2010s, this did not stop these dynamics, as there is a significant increase between 2014 and 2018. The up to $500 annual support for low income earners does not seem to induce essential wealth gains for the lower end of the distribution.
Despite these absolute differences, households at the top did not increase their overall share of Superannuation wealth. In Appendix G, I provide the normalized concentration curves for 2002 and 2018. It shows that the concentration curves are not significantly different in 2018 compared to 2002. Nevertheless, the top 20 percent hold nearly 60 percent of the overall Superannuation wealth. Given that this can be transferred from one generation to the next, these differences can accumulate over time and may contribute more to inequality in the future. I discuss this in more detail in the next section.

Life Cycle Patterns
This subsection describes wealth aggregates along age patterns. As age pension wealth affects retired households, the first part focuses on wealth levels and inequalities for different birth cohorts of the retired population. The second part takes the whole population into account. The individual age determines the stage of wealth accumulation over the life cycle. Following the neoclassical theory, individuals choose their saving rate to smooth their consumption over time. Previous research shows an inverted u-shaped pattern of wealth accumulation throughout an individual's life, with an increase throughout the working life and a decline, once an individual retires (Atkinson, 1971;Davies and Shorrocks, 2000).
Retiring population The HILDA panel data allows me to analyze the retired population from another angle, by following different birth cohorts over time. A comparison of households at the start of their retirement phase is interesting for several reasons. First, a comparison of augmented wealth levels between wealth cohorts can indicate long-term trends. Second, at that point in time in the life cycle, pension wealth is normally at its peak. As the present value of social security pension wealth depends on the individual life expectancy, it is by construction, the highest at the very beginning of retirement. Third, Superannuation accounts can then be accessed and dissaved.
Three panels in Figure 7 show the mean values of wealth aggregates for different cohorts. wealth for the 1940 to 1943 cohort increases in 2014. As described above, this is affected by the raise of the female retirement age. Even though the cohorts are strictly over the retirement age, the panels provide a household perspective, hence, this can still affect spouses of retired household heads. Superannuation wealth for retiring cohorts was nearly tripled during the 16 year period.
In the last panel, I depict some distributional insights. As I am analyzing subgroups, I use the Theil index, which is decomposable by subgroups, to describe change of augmented wealth inequality between the birth cohorts over time. Interestingly, the initial inequality remains relatively stable in each wave. There does not seem to be an increase in inequality over time for those entering the retirement phase. During retirement, the inequality in each subgroup, however, rises. This effect is not surprising: while social security pension wealth declines, its equalizing effect on augmented wealth also diminishes gradually.
I conclude that retiring households realized significant wealth gains between 2002 and 2018. This is highly driven by increasing Superannuation wealth.
Wealth and age: full population Broadening the perspective to the full population, I provide augmented wealth over age profiles in Figure 8, again with age referring to the household head. I calculate the mean wealth of 21 age cohorts. Each age cohort includes three years of age, for instance, household heads at the age 22 to 24 in the second age cohort. 42 The last age cohort comprises of all households with a household head at the age 80 or older. I plot the results for each wave using LOWESS regressions. 43 In the four panels, I depict augmented -, social security pension -, Superannuation -, and housing wealth. 42 The first cohort includes 4 years, aged 18-21. 43 Scatter plots with bootstrapped standard error for the years 2002 and 2018 are provided in Figure A5 in Appendix H.
Augmented wealth follows the same pattern in all considered waves, starting at a level close to 0 at the beginning of the life cycle and then a steady increase until the 60s, after which mean wealth values start to decline again. The estimates show, that the large increase of wealth between 2002 and 2006 seems to evaluate the wealth of those in their 50s and above. In the years 2010 and 2014, augmented wealth stagnated at the 2006 levels for all age cohorts. In 2018 augmented wealth increases again for older age cohorts, while the difference for those below their 50s is small.  While the patterns of social security pension wealth are very persistent over time, the plots confirm the previous finding that Superannuation wealth and housing wealth drive the increase of augmented wealth in these periods. Pension wealth from social security schemes starts to grow at the age of 50 in all years and then continuously increases almost linearly until the late 70s cohorts. There are other social security pension schemes included, e.g. the Service Pension or Disability Pension, which explains the take off before the 60s.
Social security wealth in 2018 appears to be slightly lower then in the cohorts before, but the difference is not significant. Superannuation wealth follows an inverted u-shaped pattern across the age cohorts and grows in every wave, but less during the time of the GFC.
The increase of Superannuation wealth between 2014 and 2018 is interesting, as several changes and economic factors interact in this period. The rise of the preservation age potentially increased wealth levels, as the accumulation phase was prolonged. The reduced concessional rate, established in the 2010s, however, could have reduced accumulation patterns. Well performing financial markets in that period potentially offset effects on the accumulation rates and raised wealth for all cohorts. In the cross section, mean wealth reduces for households with a household head above the retirement age. Mean values for household heads 80 or older get closer to zero for the waves 2002, 2006, and 2010, but remain at above $100,000 in the last two waves.
Housing wealth increases throughout the life cycle as home-ownership becomes more and more relevant. Home-ownership did not change significantly across age cohorts 44 . The increase is, therefore, fully attributable to increasing housing values. Another concern is the divergence in tax advantages along the distribution. As discussed above, the tax advantage is at 4 percent for the lowest tax rate, and 30 percent at the highest margin. As indicated in this paper, retirees at the lower end of the wealth distribution dissave Superannuation faster and potentially drop out of the scheme completely. This will ultimately increase the dispersion between retirees receiving Age Pension and those using Superannuation accounts. 44 A graph is provided in Appendix H.

Superannuation and inequality
Naturally, my analysis is not sufficient to provide clear predictions. Even though the Superannuation scheme successfully supported intra-generational wealth accumulation for many Australians, these considerations on inter -generational transfers and taxation may lead to increasing inequality in the future.
Pension wealth by characteristics Focusing on 2018, I provide pension wealth by household characteristics along age cohorts. This adds to the general understanding of pension wealth dynamics in the population. The results are shown in Figure 9. The left panels depict social security pension wealth, the right panels represent Superannuation wealth. I start with differentiating between single and couple households. To make wealth levels more comparable, I divide the couples' wealth by two. The panels show that social security pension wealth is relatively similar for coupled households, which means in regard to the per head perspective, couples hold considerably less social security pension wealth.
It reflects the proportionally lower payments and stricter thresholds of the Age Pension scheme for couples compared to two single households. In terms of wealth in Superannuation accounts, couples hold more Superannuation wealth per head than single couples. I am not able to disentangle the dynamics behind it, whether they receive less pension due to higher amounts of Superannuation, or save more, as they expect a lower pension.
Nevertheless, it indicates another interaction between the two schemes.
I also show differences between genders. Social security pension wealth is held at equal levels by female and male household heads. Superannuation accounts show no difference during the accumulation period, but start do diverge in the 60s. Both are interesting findings. This panel cannot detect child birth "penalties" for women, even though contributions are conditioned on labor market participation. This does not mean that the penalties do not exist. As this is a household perspective, these effects are potentially mitigated by partners in the household. The divergence during retirement age cannot be explained by higher dissaving rates, as I could not find a significant difference between men and women in my analysis above. Men seem to accumulate Superannuation wealth several years longer than women and, therefore, hold more wealth in their accounts.
Finally I compare pension wealth between households who own their main household residence (HMR) with those who do not. Those who do not own their HMR hold more social security pension wealth, but the difference is small. In terms of wealth in Superannuation accounts, HMR owners hold much more wealth than their counterparts. The result is striking: those households who do not own their primary home are also considerably worse off in terms of pension wealth. 45 This raises concerns about how housing wealth is treated in the Age Pension asset test. Those who do not own their home potentially do not benefit from comparably higher thresholds. Reforming Age Pension in that matter could offset some of the differences in retirement.

Augmented Wealth in an International Comparison
Augmented wealth is a helpful tool to enhance the comparability of wealth data between countries, as it reduces the bias from different social security pension schemes. This allows me to compare Australian wealth inequality with Germany, the US (Bönke et al., 2019), and Switzerland (Kuhn, 2020). Comparison of Descriptive Statistics I start with the comparison of mean values and several quintiles of the wealth aggregates w10, w12, w13, and w15 in Table 11. Regarding the mean net worth in Australia, at 324,664 USD, it is considerably higher than in Germany (182,329 USD) and Switzerland (223,525 USD) and slightly below the US (337,570 USD). However, mean social security pension wealth is 4.2 times higher in Germany, 2.6 in Switzerland, and 3.4 times higher in the US. The mean value in Superannuation accounts is higher than those of the occupational and private pension schemes in Germany or Switzerland but lower than the one in the US. Consequently augmented wealth in Australia sits at a mean value of 489,405 USD, which is above the one of Germany (472,401 USD) and Switzerland (451,294 USD) and below the US (652,504 USD). Augmented wealth in Australia is lower at the lower end of the wealth distribution, i.e. at the 25th percentile, than in the other countries.
The statistics reveal the differences between the social security pension schemes. As it is only accessible for the retired population in Australia, it accounts for only 21.29 percent of the overall population in 2014. As described above, this is mainly due to the different pension concepts. Two-thirds of the Australian Pension wealth comes, on average, from Superannuation accounts, with 84.33 percent of the households holding some wealth here.
The coverage is considerably higher than in the other countries and can be explained by 46 In German: "Berufliche Vorsorge" 47 Kuhn (2020) does not provide information on this, but the SILC survey asks generally for overall wealth, which potentially includes vehicles. Hence, the estimates from Switzerland potentially include slightly more wealth types than the other countries.  characteristics, I also find that couples hold considerably less social security pension wealth and hold more Superannuation wealth. Women seem to hold less Superannuation wealth in retirement, and home owners are also better off in terms of pension wealth.
In an international comparison, Australia exhibits relatively high values of net worth, but relatively low values of pension wealth. Net worth is more equally distributed than in Germany, Switzerland or the US. However, adding pension wealth reduces the Gini coefficient less than in the other countries, so that augmented wealth in Australia is less equally distributed than in Germany and Switzerland. The main reason for this, is the meanstested social security pension wealth, which covers only retired Australian households and is not an asset for those still in employment. This also shows the limits of the accrual method in Australia. Moreover, one could include other factors of individual welfare at retirement, as some countries provide considerably more public goods for retirees than others. In conclusion, this article represents a first analysis of the Australian pension schemes and their interaction with augmented wealth, leaving room for further assessments in the future.  Notes: Table provides the regression results of the OLS regression (1), the estimates of the Fractional Probit Model (2), and the marginal effect at means (3). Wealth variables are divided by 100,000. Robust standard errors are provided in brackets. The R 2 in (2) represents the pseudo-R 2 of the fractional probit model. The significance levels are reported with * p < 0.05, * * p < 0.01, and * * * p < 0.001. Source: Regression are based on the HILDA dataset.

E Gini Decomposition
My analysis comprises a factor decomposition to study the contribution of net worth and the pension wealth components to the overall inequality of augmented wealth in every survey year. This decomposition allows me to evaluate the interaction between the changes in pension wealth and overall augmented wealth inequality over time. Following Lerman and Yitzhaki (1985); Bönke et al. (2019), I decompose the Gini index a follows: ρa,y × Ginia,y × sa,y = A a=0 Oa,y, Where the Giniy represents the Gini index of augmented wealth in year y, ρa,y denotes the Gini correlation 49 between wealth aggregate wa,y, with a = 1, ..., A, and augmented wealth. Ginia,y is the Gini index of wealth aggregate a and sa,y the share of wealth aggregate a in augmented wealth. The product Oa,y is the absolute contribution of a wealth aggregate to overall inequality of augmented wealth. In the main analysis, I provide the relative contribution oa,y=Oa,y/Giniy. I present the results for the relative contribution of each aggregate in Figure A2. The x-axis represents the contribution of the aggregates to the augmented wealth Gini coefficient as a percentage and the y-axis depicts the years. Net worth is the highest contributor to overall augmented wealth in Australia, with a share consistently over 75 percent. The steep increase in housing wealth may explain the upward trend of the net worth aggregate between 2002 and 2006 but the change is small and not persistent.
The relative contribution from social security pension wealth reduced over the years from 5.5 percent in 2002 to 1.3 percent in 2018. On the contrary, the contribution of Superannuation wealth increased from 18.22 percent to 22.55 percent in 2018. The relative decrease of the contribution of social security pension wealth stems from a decrease in its total wealth share, showing that it did not grow as much as the other wealth aggregates. The Superannuation scheme matures throughout the 16 years time frame and increases, therefore, its distributional relevance.